you have a Lishui controller - may be worth a look inside the controller box to see if there are unused connectors.
The simplest improvement is to connect an external battery in parallel to the Gtech battery.
It may be the case that as a customer custom job with no display that the controller may still have the pcb solder points and a 5 pin lead needs soldering to the board, I can't see there being an unused wire connector being tucked in there but certainly it is worth un screwing the base top to have a look.
At 5ah the battery can only be 20 cells using 2500mah cells in 2P and likely a good 10a cell like LG HE2 OR HE4 or even the Sam 25R as the controller has a 15a max current draw. Depending on what Ian wants from the bikes use, paralleling another larger capacity battery can work. 10S 3P or 10S 4P /10ah would give Ian 10s 5/6p and 14/15ah with a battery using 2500mah - 2900mah cells would be ok
I would be inclined if going that route to moving the Gtech battery to the seat tube bottle mounts and mounting the larger new battery to the diamonds down tube.
Ian though would have two charge two batteries rather then one and both would always need to be at or very near the same voltage each time , certainly within 0.025v or less.